1. Field of the Invention
The present invention relates to a method and apparatus for digitally representing a waveform. More particularly, aspects of the invention are directed to digitally representing a waveform as phase-interleaved first and second sets of samples, the ordinates of adjacent samples differing differentially. The invention has particular application in numerically controlled oscillators.
2. Background
Numerically controlled oscillators (NCOs) are components in digital communication systems, including digital transceivers. Incorporated into a digital mixer, an NCO provides digitally controlled frequency synthesis and frequency tuning.
At its heart, an NCO includes a read only memory (ROM) lookup table that stores a waveform's peak values (ordinates) at discrete phase intervals (abscissa). When the lookup table is addressed in a predetermined sequence at a predetermined clock-rate, the lookup table outputs a sequence of peak values that discretely reconstruct the waveform at a predetermined frequency. Effectively, the lookup table maps waveform phase into amplitude at discrete intervals.
The precision of the waveform representation increases with finer phase resolution and finer amplitude quantization. However, precision comes at a cost. Finer phase resolution requires that the size of the lookup table, and hence the ROM, be increased to store more ordinates. Similarly, finer amplitude quantization requires that the size of the lookup table, and hence the ROM, be increased to store ordinates encoded with more bits.
An important design criterion is to minimize the size of the ROM lookup table, while maintaining adequate precision in representing a waveform.